Data analysis code: 

Used to calculate and plot all of the experimental figure data by processing the "scanXX###atomMatrix.mat" files stored in the data folders. 

Analysis codes are named based on the figure they are primarily used to generate, but some scripts output processed data in a separate file that is referenced in multiple figures (These cases will be listed as "Prerequisites" for any dependent files). 

Scripts with additinal files listed under "Prerequisites" require access to .mat files generated as output by the prerequisite scripts, so before attempting to run a script, ensure all prerequisites have been run at least once.

Note that get_batch_params.m contains the function get_batch_params that is called by nearly all of the other scripts.

Figure 2:

Fig2_m1_2D2_qw_n2_6Er_modfreq3_1010_phase0p5.m
Plots density profile (Fig 2A) and correlations (Fig 2B) for U = 0J, theta = 0.5pi. 
Prerequisites: None

Fig2_m1_2D2_qw_n2_6Er_modfreq3_1010_phase1p0.m
Plots density profile (Fig 2A) and correlations (Fig 2B) for U = 0J, theta = pi. 
Prerequisites: None

Fig2_m4_2D2_qw_n2_6Er_modfreq3_1010_phase0.m
Plots density profile (Fig 2A) and correlations (Fig 2B) for U = 0J, theta = 0pi. 
Prerequisites: None


Figure 3:

Fig3_m2_2D2_qw_n2_6Er_scan_phase_state_hist.m
Calculates the overlap with two specific Fock states (0011) and (1100) after short evolution time (starting from configuration 0110), as seen in Fig. 3B. 
Prerequisites: None


Figure 4:

Fig4_density_v1.m
Plots the density profiles conditioned on particle distance for three example phases (Fig. 4B).
Prerequisites: All scripts with the prefix "Fig2"

Fig4_m2023_02_27_correlations_theta_pairing_v2.m
Figure 4C and 4D, conditions quantum walk data on particle distance (d>2 and d<=2) and calculates expansion velocity by fitting rms size vs time and taking the linear slope. Plots expansion velocity vs phase for both conditioned density cases as well as the ratio of the "close" vs "far" velocities. 
Prerequisites: None


Figure 5:

Fig5_m1_2D2_qw_n2_6Er_modfreq3_990_phase_m0p5.m
Full quantum walk and correlation plot for U = 1.9J, theta = -0.5pi (Fig. 5C).
Prerequisites: None

Fig5_m2_2D2_qw_n2_6Er_modfreq3_990_phase0p5.m
Full quantum walk and correlation plot for U = 1.9J, theta = 0.5pi (Fig. 5C).
Prerequisites: None

Fig5_m1_2D2_qw_n2_6Er_modfreq3_980_scan_phase.m
Single time quantum walk at U = 2.8J for various theta, part of Fig. 5D.
Prerequisites: None

Fig5_m2_2D2_qw_n2_6Er_modfreq3_1040_scan_phase.m
Single time quantum walk at U = -2.8J for various theta, part of Fig. 5D.
Prerequisites: None

Fig5_m1_2D2_qw_6Er_modfreq3_1040_phase_m1p0.m
Single time quantum walk at U = -2.8J for theta = -pi, part of Fig. 5D.
Prerequisites: None

Fig5_delta_N_vs_phase.m
Compiles the above data to produce Fig 5D.
Prerequisites: 	Fig5_m1_2D2_qw_n2_6Er_modfreq3_980_scan_phase.m							Fig5_m2_2D2_qw_n2_6Er_modfreq3_1040_scan_phase.m
		Fig5_m1_2D2_qw_6Er_modfreq3_1040_phase_m1p0.m

Fig5_m1_effective_U_modfreq3_1070_CK_DC.m
Single time quantum walk at U = -5.7J for theta = 0.5 pi and -0.5 pi, part of Fig. 5E.
Prerequisites: None

Fig5_m1_effective_U_phase_0p5_error_Delta_N.m
Single time quantum walk at theta = 0.5pi for various U, part of Fig. 5E.
Prerequisites: None

Fig5_m1_effective_U_phase_m0p5_error_Delta_N.m
Single time quantum walk at theta = -0.5pi for various U, part of Fig. 5E.
Prerequisites: None

Fig5_delta_N_vs_U.m
Compiles above data to produce Fig. 5E.
Prerequisites: 	Fig5_m1_effective_U_phase_m0p5_error_Delta_N.m
		Fig5_m1_effective_U_phase_0p5_error_Delta_N.m
		Fig5_m1_effective_U_modfreq3_1070_CK_DC.m


Supplementary materials:

FigS1_postselection.m
Prerequisites:	Fig5_m1_effective_U_phase_0p5_error_Delta_N.m
		Fig5_m1_effective_U_modfreq3_1070_CK_DC.m
		Fig2_m1_2D2_qw_n2_6Er_modfreq3_1010_phase1p0.m

FigS2_m1_Bloch_oscillations_freq1_780Hz.m
Prerequisites: None

FigS6_m1_2D2_qw_n2_6Er_phase0_scan_U_error_Delta_N.m
Prerequisites: None

FigS7_m1_2D2_qw_n2_6Er_modfreq3_1010_phase0p25.m
Plots density profile and correlations for U = 0J, theta = 0.25pi shown in Fig S7. 
Prerequisites: None

FigS7_m2_2D2_qw_n2_6Er_modfreq3_1010_phase0p75.m
Plots density profile and correlations for U = 0J, theta = 0.75pi shown in Fig S7. 
Prerequisites: None